There's no simple way to talk about
The Birth of Tragedy. As many note, it's "a young man's work;" Nietzsche felt compelled to write it, and equally compelled, many years later, to take it apart, regretting especially sections 16 - 25 which foretell a German cultural rebirth, thanks to the midwifely exertions of Richard Wagner in the wake of Immanuel Kant and Arthur Schopenhauer.
What's clear is that in writing it, Nietzsche was committing professional suicide, as Marianne Cowan notes in her intro to
Philosophy in the Tragic Age of the Greeks:
The Birth of Tragedy presented a view of the Greeks so alien to the spirit of the time and to the ideals of its scholarship that it blighted Nietzsche's entire academic career. It provoked pamphlets and counter-pamphlets attacking him on the grounds of common sense, scholarship and sanity. For a time, Nietzsche, then a professor of classical philology at the University of Basel, had no students in his field. His lectures were sabotaged by German philosophy professors who advised their students not to show up for Nietzsche's courses. WP
It seems fair to say that Nietzsche wrote under the pressure of several enthusiasms: for Greek culture (especially early tragedy); for music (especially that of Wagner); for epistemological questions (represented mainly by Kant); as well as by several critical obsessions -- a detestation of his contemporary German world of newspapers, politics, "Alexandrian" music and decadent sensibility.
So he tells us a story of the birth of an art form - tragedy - out of the spirit of another art form - music. What follows is merely an effort to describe and summarize his argument.
Nietzsche referred to the nature of the relation of Apollo and Dionysus as "the capital question"
(die Hauptfrage). In Nietzsche's story, they tend to be associated with a variety of artistic and cultural polarities, e.g., painting vs. music, verbal differentiation vs. harmonic unity, the power of statement vs. the power of voice, culture vs. nature, science vs. art, prose vs. poetry, classic vs. romantic, spatial vs. temporal, eye vs. ear, stillness vs. motion, recognition vs. revelation, contemplation vs. action, figurative vs. proper* meaning, and the like.
The Apollonian dream is an unavoidable, uncontrolled response (it holds out "the head of Medusa" (sect. 2)) that shelters us from the sheer annihilative power of Dionysus. At the heart of Greek tragedy is the chorus of dancing satyrs -- not optimistic middle-class cafe goers -- who are rapt in an apprehension of the God who dissolves all that is, and because that apprehension is intolerable, a dreamlike realm of extraordinary beauty is thrown up as a shield -- the tragic hero and his tale, on the stage.
So we have the originary progenitor, Dionysus, only apprehended through music, who fathers, or causes, the counterblow of the plastic, visual realm of the Apollonian. In tragedy these two art forms, or modes, strike a balance that is perfect in Aeschylus, already slipping in Sophocles, and, by the time of Euripides, whom Nietzsche accuses along with Socrates of destroying music, is thoroughly debased.
Just as Euripides reduced the gods and heroes from mythic stature to characters not unlike ourselves in his plays, Socrates placed the word, the intellect, the logic and method of scientific inquiry above the wild dance of the satyrs, and has led us on a voyage of discovery unlike anything that came before. Socrates is the major articulation in Nietzsche's "history," since he at once ends the glory days of Dionysus and Apollo, and begins the voyage of the scientific mind.
Science gives us the world made over in an image the human mind can fathom. But look around us, Nietzsche says -- do we see a culture that nourishes Homeric visions and Aeschylean magic? Something important has been left out -- ignored, suppressed, or destroyed -- along the way. In section 15, the original ending of the book, the good ship Socrates runs into trouble:
But science, spurred by its powerful illusion, speeds irresistibly toward its limits where its optimism, concealed in the essence of logic, suffers shipwreck. For the periphery of the circle of science has an infinite number of points; and while there is no telling how this circle could ever be surveyed completely, noble and gifted men nevertheless reach, e'er half their time and inevitably, such boundary points (Grenzpunkte) on the periphery from which one gazes into what defies illumination. When they see to their horror how logic coils up at these boundaries and finally bites its own tail -- suddenly the new form of insight breaks through, tragic insight which, merely to be endured, needs art as a protection and remedy. (Kaufmann trans. p. 97-98).
Nun aber eilt die Wissenschaft, von ihrem kräftigen Wahne angespornt, unaufhaltsam bis zu ihren Grenzen, an denen ihr im Wesen der Logik verborgener Optimismus scheitert. Denn die Peripherie des Kreises der Wissenschaft hat unendlich viele Punkte, und während noch gar nicht abzusehen ist, wie jemals der Kreis völlig ausgemessen werden könnte, so trifft doch der edle und begabte Mensch, noch vor der Mitte seines Daseins und unvermeidlich, auf solche Grenzpunkte der Peripherie, wo er in das Unaufhellbare starrt. Wenn er hier zu seinem Schrecken sieht, wie die Logik sich an diesen Grenzen um sich selbst ringelt und endlich sich in den Schwanz beisst - da bricht die neue Form der Erkenntniss durch, die tragische Erkenntniss, die, um nur ertragen zu werden, als Schutz und Heilmittel die Kunst braucht. Project Gutenberg EBook.
A few interpretive comments: Nietzsche tells a story of origin which becomes a story of destiny. The logic of his narrative presents Apollo, Dionysus, and Socrates as three interrelated entities who are necessary to each other even as they remain, in various and not simple ways, antagonists. Smiling Socrates ended the tragic Dionysian era, and at the end of his scientific quest, inevitably (
unvermeidlich), lies the horror that lay behind the glorious culture he killed, auguring a new tragic culture on the horizon.
In the sections following 15 we hear strains of another Nietzsche -- not the cool analytic philologist or gifted philosopher of aesthetics, but Nietzsche the scathing critic of contemporary society. A prophetic note enters as he foresees a new beginning in which Germany is to play a central role. We may sense that the book founders at this point, but it seems doomed to do by the structure of its argument. Like the head of the ourobouros, the seeds of that future rebirth are there from the beginning of his tale.
*This particular polarity is made much of by
Paul de Man.
, which now exists in English translation under that title. In it he addresses 
